Essay

audio processing

Essay specific features

Essay content:

Then $ x(t)$ can be exactly reconstructed from its samples $ x_d(n)$ if $ X(j\omega)=0$ for all $ \vert\omega\vert\geq\pi/T$.D.3 Proof: From the continuous-time aliasing theorem (§D.2), we have that the discrete-time spectrum $ X_d(e^{j\theta})$ can be written in terms of the continuous-time spectrum $ X(j\omega)$ as $\displaystyle X_d(e^{j\omega_d T}) = \frac{1}{T} \sum_{m=-\infty}^\infty X[j(\omega_d +m\Omega_s )] $ where $ \omega_d \in(-\pi/T,\pi/T)$ is the ``digital frequency'' variable...
displayed 300 characters

If $ X(j\omega)=0$ for all $ \vert\omega\vert\geq\Omega_s /2$, then the above infinite sum reduces to one term, the $ m=0$ term, and we have $\displaystyle X_d(e^{j\omega_d T}) = \frac{1}{T} X(j\omega_d ), \quad \omega_d \in\left(-\frac{\pi}{T},\frac{\pi}{T}\right) $ At this point, we can see that the spectrum of the sampled signal $ x(nT)$ coincides with the nonzero spectrum of the continuous-time signal $ x(t)$...
displayed 300 characters

General issues of this essay:

Related essays:

• The Chinese Connection: Reconstructing Masculinity through Adversity

    2 pages,   542 words
   
   
• Circular Motion Labs

    2 pages,   401 words
   
   
• Eating fish is healthy

    2 pages,   322 words
   
   
• Mass Density Lab

    3 pages,   768 words
   
   
• audio processing

    2 pages,   314 words
   
   
• DCCC Website

    1 pages,   275 words
   
   
• Dsp Tools Like Matlab And Gnu Octave

    2 pages,   440 words